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Equation (a11) has already determined the
coefficient *a*_{11}. Thus, (Kutwop) shows that

| |
(23) |

This relation provides a constraint on the sum of the two
generalized Biot-Willis parameters for the
double-porosity problem.
Not all of these long-time results are independent. In fact,
there are only three independent equations among the five
given above expressing the *a*_{ij} in terms
of the single-porosity (long-time) moduli.

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Stanford Exploration Project

6/8/2002